相关论文: A Hopf-Lax Type Formula for Multi-Agent Path Plann…

We develop a general theoretical framework for optimal probability density control on standard measure spaces, aimed at addressing large-scale multi-agent control problems. In particular, we establish a maximum principle (MP) for control…

Many real-world multi-agent systems exhibit nonlinear dynamics and complex inter-agent interactions. As these systems increase in scale, the main challenges arise from achieving scalability and handling nonconvexity. To address these…

We present a method for optimal path planning of human walking paths in mountainous terrain, using a control theoretic formulation and a Hamilton-Jacobi-Bellman equation. Previous models for human navigation were entirely deterministic,…

Recent results in the study of the Hamilton Jacobi Bellman (HJB) equation have led to the discovery of a formulation of the value function as a linear Partial Differential Equation (PDE) for stochastic nonlinear systems with a mild…

We address two major challenges in scientific machine learning (SciML): interpretability and computational efficiency. We increase the interpretability of certain learning processes by establishing a new theoretical connection between…

In this paper we present a new algorithm for the solution of Hamilton-Jacobi-Bellman equations related to optimal control problems. The key idea is to divide the domain of computation into subdomains which are shaped by the optimal dynamics…

The path-integral control, which stems from the stochastic Hamilton-Jacobi-Bellman equation, is one of the methods to control stochastic nonlinear systems. This paper gives a new insight into nonlinear stochastic optimal control problems…

Multi-robot task planning requires decomposing natural-language instructions into executable actions for heterogeneous robot teams. Conventional Planning Domain Definition Language (PDDL) planners provide rigorous guarantees but struggle to…

This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a…

Multi-Agent Path Finding (MAPF) focuses on determining conflict-free paths for multiple agents navigating through a shared space to reach specified goal locations. This problem becomes computationally challenging, particularly when handling…

The majority of methods used to compute approximations to the Hamilton-Jacobi-Isaacs partial differential equation (HJI PDE) rely on the discretization of the state space to perform dynamic programming updates. This type of approach is…

We treat infinite horizon optimal control problems by solving the associated stationary Hamilton-Jacobi-Bellman (HJB) equation numerically to compute the value function and an optimal feedback law. The dynamical systems under consideration…

Computing optimal feedback controls for nonlinear systems generally requires solving Hamilton-Jacobi-Bellman (HJB) equations, which are notoriously difficult when the state dimension is large. Existing strategies for high-dimensional…

This paper proposes a highly robust autonomous agent framework based on the ReAct paradigm, designed to solve complex tasks through adaptive decision making and multi-agent collaboration. Unlike traditional frameworks that rely on fixed…

We present a finite dimensional variational model for multi-agent path-planning in which a group of agents traverses from initial positions to a target distribution in a moving medium. The model is derived using the agent-based formulation…

Multi-agent pathfinding (MAPF) is a widely used abstraction for multi-robot trajectory planning problems, where multiple homogeneous agents move simultaneously within a shared environment. Although solving MAPF optimally is NP-hard,…

We propose a novel data-driven neural network (NN) optimization framework for solving an optimal stochastic control problem under stochastic constraints. Customized activation functions for the output layers of the NN are applied, which…

We study the optimal control of path-dependent piecewise deterministic processes. An appropriate dynamic programming principle is established. We prove that the associated value function is the unique minimax solution of the corresponding…

This work considers the problem of optimal lane changing in a structured multi-agent road environment. A novel motion planning algorithm that can capture long-horizon dependencies as well as short-horizon dynamics is presented. Pivotal to…

Presented is a method to compute certain classes of Hamilton-Jacobi equations that result from optimal control and trajectory generation problems with time delays. Many robotic control and trajectory problems have limited information of the…